Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 15 1 2024 01 01 Reliability analysis of lifetime systems based on Weibull distribution 321 329 8428 10.22075/ijnaa.2024.31309.4609 EN Mohammadreza Shahriari Faculty of Industrial Management, South Tehran Branch, Islamic Azad University, Tehran, Iran Hooman Shahrasbi Department of Economics, Management, industrial Engineering and Tourism, University of Aveiro, Aveiro, Portugal Arash Zaretalab Department of Business Management, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran Journal Article 2023 07 19 Reliability analysis is crucial for understanding the performance and failure characteristics of lifetime systems. This paper presents a comprehensive study on the reliability analysis of lifetime systems using the Weibull distribution. The Weibull distribution, known for its flexibility in modeling failure times, provides a versatile framework for capturing diverse failure behaviors. A useful model for redundancy systems is proposed in this paper. The model consists of $(n+1)$ components, where n components serve as spare parts for the main component. The failure rate of the working component is time-dependent, denoted as $\lambda (t)$, while the failure rates of the non-working components are assumed to be zero. Whenever a component fails, one of the spare parts immediately takes over its role. The failed components in this model are considered non-repairable. To analyze this model, we establish the differential equations that describe the system states. By solving these equations, we calculate important parameters such as system reliability and mean time to failure (MTTF) in real-time scenarios. These parameters provide valuable insights into the performance and behavior of the system under study. By employing the Weibull distribution and the proposed model, this paper contributes to enhancing the understanding of reliability analysis in lifetime systems and enables the estimation of important reliability parameters for practical applications. https://ijnaa.semnan.ac.ir/article_8428_bae8274768e217d994b58d624b2c4769.pdf